1、δz=aδx+bδy+0(ρ)

2、δz=f(x+δx，y+δy)-f(x，y)

Take formula 2, (1-0.2)/(2+0.1)-1/2 =-0.1/9.

Two formulas of total differential:

1、dz=(？ z/？ x)δx+(？ z/？ y)δy

2、dz=(？ z/？ x)dx+(？ z/？ y)dy

Take 1 formula? z/？ x=(-y)/x^2=- 1/4？ z/？ Y= 1/x= 1/2, and (-1/4) * 0.1+(-0.2) *1/2 =-0.1.

Common methods of mathematical derivation

Common conclusion: (ln | x |)' =1/X.

Shaped like y=(x-a? )(x-a？ ) ... (x-an) or y=(x-a? )(x-a？ )...(x-an)/(x-b？ )(x-b？ (x-bn) can be transformed into algebraic sum form by taking natural logarithm on both sides.

Unreasonable functions or functions in the form of y=x to the power of x, such as taking the natural logarithm of y=x to the power of x, can be transformed into y=lnx, y/y = lnx+x *1/x = > y ' = ylnx+y = & gt； Y'=x to the x power lnx+x to the x power.